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Day 345: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Application of Derivatives. Asked once: 2021 Paper 10 (same type asked 6 times) See all 6 of this type

    85
    Let P(x)P(x) be a real polynomial of degree 3 which vanishes at x=−3x= - 3. Let P(x)P(x) have local minima at x=1x = 1, local maxima at x=−1x = - 1 and ∫−11P(x)dx=18\int_{- 1}^{1} P(x)dx = 18, then the sum of all the coefficients of the polynomial P(x)P(x) is equal to

  2. Question 2

    Inverse Trigonometric Functions. Asked once: 2021 Paper 12 (same type asked 6 times) See all 6 of this type

    40
    The value of tan⁡(2tan⁡−1(35)+sin⁡−1(513))\tan\left( 2\tan^{- 1}\left( \frac{3}{5} \right)+\sin^{- 1}\left( \frac{5}{13} \right) \right) is equal to :

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  3. Question 3

    Complex Numbers. Asked once: 29 Jan 2023 (same type asked 6 times) See all 6 of this type

    178
    Let α=8−14i,A={z∈C:αz−αˉzˉz2−(zˉ)2−112i=1}\alpha = 8 - 14i,A =\left\{ z\in C:\frac{\alpha z -\bar{\alpha}\bar{z}}{z^{2}- (\bar{z})^{2}- 112i}= 1 \right\} and B={z∈C:∣z+3i∣=4}\mathbf{B = \{ z \in C:|z + 3i| = 4\}}. Then ∑z∈A∩B(Rez−Imz)\sum_{z \in A \cap B} (Rez - Imz) is equal to

  4. Question 4

    Matrices. Asked once: 31 Jan 2023 (same type asked 6 times) See all 6 of this type

    172
    Let AA be a n×nn \times n matrix such that ∣A∣=2|A| = 2. If the determinant of the matrix Adj(2⋅Adj(2 A−1))⋅Adj\left( 2 \cdot Adj\left( 2{\text{ }A}^{- 1} \right) \right)\cdot is 2842^{84}, then nn is equal to

  5. Question 5

    Permutations and Combinations. Asked once: 1 Feb 2023 (same type asked 6 times) See all 6 of this type

    178
    Number of integral solutions to the equation x+y+z=21x + y + z = 21, where x≥1,y≥3,z≥4x \geq 1,y \geq 3,z \geq 4, is equal to